Asymptotic GIT-stability of KSB-stable varieties

We prove that KSB-stable varieties introduced by Kollár and Shepherd-Barron as a generalization of Deligne-Mumford's stable curves are stable in the sense of geometric invariant theory (GIT). More precisely, we show that KSB-stable varieties are asymptotically GIT-stable with respect to a sequence of linearizations defined by the Hodge bundle.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40583
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

Asymptotic GIT-stability of KSB-stable varieties

Behrouz Taji, Sándor J. Kovács
arXiv (Cornell University)
Algebraic Geometry and Number Theory
preprint

Asymptotic GIT-stability of KSB-stable varieties

Behrouz Taji, Sándor J. Kovács
preprint en

Abstract

We prove that KSB-stable varieties introduced by Kollár and Shepherd-Barron as a generalization of Deligne-Mumford's stable curves are stable in the sense of geometric invariant theory (GIT). More precisely, we show that KSB-stable varieties are asymptotically GIT-stable with respect to a sequence of linearizations defined by the Hodge bundle.

arXiv (Cornell University)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Asymptotic GIT-stability of KSB-stable varieties — Behrouz Taji, Sándor J. Kovács · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS